System Description: LEO - A Higher-Order Theorem Prover

@inproceedings{Benzmller1998SystemDL,
  title={System Description: LEO - A Higher-Order Theorem Prover},
  author={Christoph Benzm{\"u}ller and Michael Kohlhase},
  booktitle={CADE},
  year={1998}
}
Many (mathematical) problems, such as Cantor’s theorem, can be expressed very elegantly in higher-order logic, but lead to an exhaustive and un-intuitive formulation when coded in first-order logic. Thus, despite the difficulty of higher-order automated theorem proving, which has to deal with problems like the undecidability of higher-order unification (HOU) and the need for primitive substitution, there are proof problems which lie beyond the capabilities of first-order theorem provers, but… 
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The three new calculi ER, ERUE, EP and ERUE which improve the mechanisation of defined and primitvie equality in classical type theory and these calculi reach Henkin completeness without requiring additional extensionality axioms are introduced.
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This work has shown in the past that higher-order reasoning systems can solve problems of this kind automatically, but the complexity inherent in their calculi and their inefficiency in dealing with large numbers of clauses prevent these systems from solving a whole range of problems.
System Description: LEO -- A Resolution based Higher-Order Theorem Prover
TLDR
The Leo system has recently been successfully coupled with a first-order resolution theorem prover (Bliksem) and is implemented as part of the Ωmega environment and has been integrated with theΩmega proof assistant.
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A Lost Proof
We re-investigate a proof example presented by George Boolos which perspicuously illustrates Gödel’s argument for the potentially drastic increase of proof-lengths in formal systems when carrying
LEO-II - A Cooperative Automatic Theorem Prover for Classical Higher-Order Logic (System Description)
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The improved performance of LEO-II, especially in comparison to its predecessor LEO, is due to several novel features including the exploitation of term sharing and term indexing techniques, support for primitive equality reasoning, and improved heuristics at the calculus level.
Fast Clause Normalization for Higher-Order Automated Theorem Proving
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The task is to develop a new and ideally improved OANTS architecture for the new LEO-II prover, which is currently using a primitive, sequential interaction model.
Functions-as-Constructors Higher-Order Unification
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The main idea behind this extension is that the arguments to a higher-order, free variable can be more than just distinct bound variables: they can also be terms constructed from (sufficient numbers of) such variables using term constructors and where no argument is a subterm of any other argument.
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